Lithium-air batteries (LABs) are expected to provide a cell with a much higher capacity than ever attained before, but their prototype cells present a limited areal cell capacity of no more than 10 mAh cm-2, mainly due to the limitation of their air electrodes. Here, we demonstrate the use of flexible carbon nanotube (CNT) sheets as a promising air electrode for developing ultra-high capacity in LAB cells, achieving areal cell capacities of up to 30 mAh cm-2, which is approximately 15 times higher than the capacity of cells with lithium-ion battery (LiB) technology (~2 mAh cm-2). During discharge, the CNT sheet electrode experienced enormous swelling to a thickness of a few millimeters because of the discharge product deposition of lithium peroxide (Li2O2), but the sheet was fully recovered after being fully charged. This behavior results from the CNT sheet characteristics of the flexible and fibrous conductive network and suggests that the CNT sheet is an effective air electrode material for developing a commercially available LAB cell with an ultra-high cell capacity.